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<p>Morphing-wing unmanned aerial vehicles reshape their wings in flight to reconcile conflicting mission profiles. This reshaping induces large, rapid variations in inertia and aerodynamic coefficients that make longitudinal stabilisation difficult. Conventional linear parameter varying gain-scheduled controllers bound the input/output gain but do not quantify the steady-state tracking error under unmodelled perturbations and actuator saturation. We close this gap with a hybrid controller of two parts. An Enhanced Structural Proportional-Integral baseline that augments the gain-scheduled law with back-calculation anti-windup, adaptive integral action, morphing-rate feedforward, and pitch-speed cross-coupling; and a physics-structured dynamic compensator built on a closed-form continuous-time recurrence whose weights are fixed by a sign-constrained design rather than trained on data, keeping the compensator interpretable and its stability certificate exact. We prove a parameter-dependent Lyapunov inequality with a rate-bounded derivative that yields a closed-form ultimate bound on the tracking error, certified first on a scheduling grid and then strengthened to a strictly global certificate over the scheduling polytope through a vertex semidefinite feasibility problem. The compensator carries a closed-form contraction certificate together with an input-to-state stability bound. In Monte-Carlo experiments with <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\pm 30\%\)</EquationSource></InlineEquation> aerodynamic uncertainty, the controller reduces root mean square pitch error by over <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(27\%\)</EquationSource></InlineEquation>, overshoot by over <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(31\%\)</EquationSource></InlineEquation>, settling time by over <InlineEquation ID="IEq4"><EquationSource Format="TEX">\(55\%\)</EquationSource></InlineEquation>, and throttle total variation by over <InlineEquation ID="IEq5"><EquationSource Format="TEX">\(81\%\)</EquationSource></InlineEquation> relative to the historical baseline, at a per-step computational cost compatible with embedded execution.</p>

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Hybrid gain-scheduled PI control with a closed-form contraction compensator for longitudinal stabilisation of morphing-wing UAVs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月16日

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  • Christian-Marie Moanda Ndeko Mosengo,
  • Hongwei Mo,
  • Patrick Kibambe Kitenge,
  • Landry Mpuate Lekekian,
  • Elise Kasereka Kiombwe

摘要

Morphing-wing unmanned aerial vehicles reshape their wings in flight to reconcile conflicting mission profiles. This reshaping induces large, rapid variations in inertia and aerodynamic coefficients that make longitudinal stabilisation difficult. Conventional linear parameter varying gain-scheduled controllers bound the input/output gain but do not quantify the steady-state tracking error under unmodelled perturbations and actuator saturation. We close this gap with a hybrid controller of two parts. An Enhanced Structural Proportional-Integral baseline that augments the gain-scheduled law with back-calculation anti-windup, adaptive integral action, morphing-rate feedforward, and pitch-speed cross-coupling; and a physics-structured dynamic compensator built on a closed-form continuous-time recurrence whose weights are fixed by a sign-constrained design rather than trained on data, keeping the compensator interpretable and its stability certificate exact. We prove a parameter-dependent Lyapunov inequality with a rate-bounded derivative that yields a closed-form ultimate bound on the tracking error, certified first on a scheduling grid and then strengthened to a strictly global certificate over the scheduling polytope through a vertex semidefinite feasibility problem. The compensator carries a closed-form contraction certificate together with an input-to-state stability bound. In Monte-Carlo experiments with \(\pm 30\%\) aerodynamic uncertainty, the controller reduces root mean square pitch error by over \(27\%\), overshoot by over \(31\%\), settling time by over \(55\%\), and throttle total variation by over \(81\%\) relative to the historical baseline, at a per-step computational cost compatible with embedded execution.